In this paper the technique of algorithm-based fault tolerance which is used to detect and correct transient or permanent hardware faults by checksum matrices is reconsidered for triangular systolic arrays. Linear err...
详细信息
In this paper the technique of algorithm-based fault tolerance which is used to detect and correct transient or permanent hardware faults by checksum matrices is reconsidered for triangular systolic arrays. Linear error detecting arrays are developed for both matrix product and triangular factorisation and are shown to interface neatly with triangular schemes. The overheads associated with error detecting redundancy is offset by hardware reduction due to the folding of the array to produce triangular rather than the standard hex connected arrays. The result is shown to be improved efficiency and area efficient fault tolerant arrays.
We obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums Sn = n-ary sumation nj=1 xi j,n of triangular arrays {xi 1,n, xi 2,n, . . . , xi n,n} satisfyi...
详细信息
We obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums Sn = n-ary sumation nj=1 xi j,n of triangular arrays {xi 1,n, xi 2,n, . . . , xi n,n} satisfying some mixing and moment conditions (which are not necessarily uniform in n). For certain classes of additive functionals of triangular arrays of contracting Markov chains (in the sense of Dobrushin) we obtain rates which are close to the best rates obtained for independent random variables. In addition, we obtain close to optimal rates in the usual CLT and a moderate deviations principle and some Rosenthal type inequalities. We will also discuss applications to some classes of local statistics (e.g. covariance estimators), as well as expanding non-stationary dynamical systems, which can be reduced to non-uniformly mixing triangular arrays by an approximation argument. The main novelty here is that our results are obtained without any assumptions about the growth rate of the variance of Sn. The result are obtained using a certain type of block decomposition, which, in a sense, reduces the problem to the case when the variance of Sn is "not negligible" in comparison with the (new) number of summands. (c) 2023 Elsevier B.V. All rights reserved.
In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics.
In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics.
In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniqu...
详细信息
In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.
We establish a strong invariance principle for triangular arrays of a broad class of weakly dependent real random variables. We approximate the original array of dependent random variables by an array of rowwise indep...
详细信息
We establish a strong invariance principle for triangular arrays of a broad class of weakly dependent real random variables. We approximate the original array of dependent random variables by an array of rowwise independent standard normal variables. We demonstrate the functional central limit theorem and law of the iterated logarithm for the approximating array and thereby extend these results to the original array. Among several examples, we look at arrays used in describing the rate of convergence of estimators in regression analysis.
We analyze the fluctuations of incomplete U-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an ...
详细信息
We analyze the fluctuations of incomplete U-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled and centered version of the U-statistic converges to a normal random variable. Our method of proof relies on a martingale CLT. An application, a CLT for the hitting time for random walks on random graphs, will be presented in Lowe and Terveer (2020).
In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel e...
详细信息
In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.
Given a triangular array a = {a(n,k), 1 = 1} of positive reals, we study the complete convergence property of T-n = Sigma(kn)(k=1)a(n,k)X(n,k) for triangular arrays X = {X-n,X-k, 1 = 1} of independent random variables...
详细信息
Given a triangular array a = {a(n,k), 1 <= k <= k(n,) n >= 1} of positive reals, we study the complete convergence property of T-n = Sigma(kn)(k=1)a(n,k)X(n,k) for triangular arrays X = {X-n,X-k, 1 <= k <= k(n), n >= 1} of independent random variables. In the Gaussian case we obtain a simple characterization of density type. Using Skorohod representation and Gaussian randomization, we then derive sufficient criteria for the case when X-n,X-k are in L-P, and establish a link between the L-P-case and L-2P-case in terms of densities. We finally obtain a density type condition in the case of uniformly bounded random variables. (c) 2007 Elsevier B.V. All rights reserved.
In this report three thinning algorithms are developed: one each for use with rectangular, hexagonal, and triangular arrays. The approach to the development of each algorithm is the same. Pictorial results produced by...
详细信息
In this report three thinning algorithms are developed: one each for use with rectangular, hexagonal, and triangular arrays. The approach to the development of each algorithm is the same. Pictorial results produced by each of the algorithms are presented and the relative performances of the algorithms are compared. It is found that the algorithm operating with the triangular array is the most sensitive to image irregularities and noise, yet it will yield a thinned image with an overall reduced number of points. It is concluded that the algorithm operating in conjunction with the hexagonal array has features which strike a balance between those of the other two arrays. [ABSTRACT FROM AUTHOR]
It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for lar...
详细信息
It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore the boundary between these two kinds of behavior. Motivation comes from the wish to construct models for the statistical analysis of extremes of background gamma radiation over the United Kingdom. The methods extend to row-wise maxima of certain triangular arrays, for which limiting distributions are also derived.
暂无评论